When the ground-services employee who stole a turboprop airliner last week declined air-traffic controllers’ piloting advice, saying he had played videogames, it was no surprise to some devotees of intricate home flight-simulation programs.

Such software can mimic many phases of aircraft operations, including takeoffs, as well as how to respond to heavy weather and emergencies, pilots and software makers say. The simulators are also more affordable than pursuing a pilot’s license and can help satisfy a lifelong obsession...